Arknights Pull Calculator

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Reviewed by: David Chen, CFA

This calculator utilizes complex probability distributions to estimate 6-star acquisition rates within the Arknights Gacha system, providing a theoretical probability for financial planning.

Plan your Headhunting efficiently! Use the Arknights Pull Calculator to determine the probability of acquiring a 6-star operator based on your current pity count and planned number of pulls.

Arknights Pull Calculator

Note: Calculation is highly accurate for C=1, theoretical for C>1.

Arknights Pull Calculator Formula

The probability of pulling at least one 6-star operator within N pulls, starting from a pity count P, is $P(\text{Success}) = 1 – P(\text{Failure})$, where $P(\text{Failure})$ is the cumulative probability of not getting a 6-star in any of the subsequent N pulls.

Let $R_i$ be the 6-star rate on pull $i$. $R_i$ depends on the total pull count $i_{total} = P + i$.

  • If $i_{total} \le 50$: $R_i = 0.02$ (2%)
  • If $i_{total} > 50$: $R_i = 0.02 + 0.02 \times (i_{total} – 50)$

The cumulative failure probability is:

$$P(\text{Failure}) = \prod_{i=1}^{N} (1 - R_i)$$

Note: The calculation assumes a successful pull resets the process, focusing on the probability of the *first* success in the next N pulls.

Formula Source:

Variables:

  • Planned Pulls (N): The total number of Headhunting pulls you intend to perform in this session.
  • Current Pity Counter (P): The number of pulls made since your last 6-star operator was acquired. This value is crucial as it dictates the starting rate.
  • Desired 6★ Copies (C): The number of 6-star operators you wish to acquire. The calculator provides the probability for the first copy (C=1).

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What is an Arknights Pull Calculator?

An Arknights Pull Calculator is an essential tool for players dedicated to optimization and resource management in the popular mobile game. It helps predict the likelihood of acquiring high-rarity operators (specifically 6-star units) within a specified number of pulls. Due to the complex, non-linear pity system in Arknights, simple percentage calculations are insufficient. This calculator integrates the step-up rate mechanism to provide a more accurate probability estimate.

Understanding your pull probability is critical for managing your Orundum and Headhunting Ticket reserves. Players can use the results to determine if they need to farm more resources, skip a banner, or commit to a specific Headhunting event, ensuring they maximize their chances for the most powerful units while maintaining resource sustainability.

How to Calculate Arknights Pull Probability (Example)

Let’s calculate the probability of getting at least one 6-star operator in 30 pulls, starting from a Pity Counter of 40.

  1. Identify Inputs: Planned Pulls (N) = 30, Current Pity (P) = 40. Target Pulls for success: 40 + 1 = 41st pull.
  2. Determine Starting Rate: Since P is 40 (less than 50), the base rate for the next pull (pull 41) is 2% (0.02).
  3. Calculate Rates for the 30 pulls (i=1 to 30):
    • Pulls 41-50 (i=1 to 10): Rate remains 2%. Failure rate is $1 – 0.02 = 0.98$.
    • Pulls 51-70 (i=11 to 30): Pity activates. Pull 51 is rate 4%. Pull 52 is 6%, etc., increasing by 2% per pull.
  4. Calculate Cumulative Failure Probability: The probability of failure is the product of all failure rates. This requires iterating through each pull, multiplying the failure probabilities: $P(\text{Failure}) = (0.98)^{10} \times (0.96) \times (0.94) \times \dots$.
  5. Final Result: $P(\text{Success}) = 1 – P(\text{Failure})$. In this example, the final probability would be approximately 98.7%.

Frequently Asked Questions (FAQ)

What is the base rate for a 6-star operator? The base probability for acquiring a 6-star operator is 2% (0.02) per pull.

How does the pity system work in Arknights? After 50 consecutive pulls without acquiring a 6-star operator, the probability of obtaining one increases by 2% with every subsequent pull until a 6-star is obtained.

Does the pity counter carry over to the next banner? Yes, the pity counter for the standard Headhunting banner (rate-up banners) typically carries over, ensuring you don’t lose progress between events.

Can I input a pity counter greater than 99? While mathematically possible, the rate hits 100% well before pull 99 (at pull 99, the rate is $0.02 + 0.02 \times 49 = 1.00$). The maximum meaningful input for the pity counter is 99.

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